Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
The United Kingdom the United Kingdom of Great Britain and Northern Ireland, sometimes referred to as Britain, is a sovereign country located off the north-western coast of the European mainland. The United Kingdom includes the island of Great Britain, the north-eastern part of the island of Ireland, many smaller islands. Northern Ireland is the only part of the United Kingdom that shares a land border with another sovereign state, the Republic of Ireland. Apart from this land border, the United Kingdom is surrounded by the Atlantic Ocean, with the North Sea to the east, the English Channel to the south and the Celtic Sea to the south-west, giving it the 12th-longest coastline in the world; the Irish Sea lies between Great Ireland. With an area of 242,500 square kilometres, the United Kingdom is the 78th-largest sovereign state in the world, it is the 22nd-most populous country, with an estimated 66.0 million inhabitants in 2017. The UK is constitutional monarchy; the current monarch is Queen Elizabeth II, who has reigned since 1952, making her the longest-serving current head of state.
The United Kingdom's capital and largest city is London, a global city and financial centre with an urban area population of 10.3 million. Other major urban areas in the UK include Greater Manchester, the West Midlands and West Yorkshire conurbations, Greater Glasgow and the Liverpool Built-up Area; the United Kingdom consists of four constituent countries: England, Scotland and Northern Ireland. Their capitals are London, Edinburgh and Belfast, respectively. Apart from England, the countries have their own devolved governments, each with varying powers, but such power is delegated by the Parliament of the United Kingdom, which may enact laws unilaterally altering or abolishing devolution; the nearby Isle of Man, Bailiwick of Guernsey and Bailiwick of Jersey are not part of the UK, being Crown dependencies with the British Government responsible for defence and international representation. The medieval conquest and subsequent annexation of Wales by the Kingdom of England, followed by the union between England and Scotland in 1707 to form the Kingdom of Great Britain, the union in 1801 of Great Britain with the Kingdom of Ireland created the United Kingdom of Great Britain and Ireland.
Five-sixths of Ireland seceded from the UK in 1922, leaving the present formulation of the United Kingdom of Great Britain and Northern Ireland. There are fourteen British Overseas Territories, the remnants of the British Empire which, at its height in the 1920s, encompassed a quarter of the world's land mass and was the largest empire in history. British influence can be observed in the language and political systems of many of its former colonies; the United Kingdom is a developed country and has the world's fifth-largest economy by nominal GDP and ninth-largest economy by purchasing power parity. It has a high-income economy and has a high Human Development Index rating, ranking 14th in the world, it was the world's first industrialised country and the world's foremost power during the 19th and early 20th centuries. The UK remains a great power, with considerable economic, military and political influence internationally, it is sixth in military expenditure in the world. It has been a permanent member of the United Nations Security Council since its first session in 1946.
It has been a leading member state of the European Union and its predecessor, the European Economic Community, since 1973. The United Kingdom is a member of the Commonwealth of Nations, the Council of Europe, the G7, the G20, NATO, the Organisation for Economic Co-operation and Development and the World Trade Organization; the 1707 Acts of Union declared that the kingdoms of England and Scotland were "United into One Kingdom by the Name of Great Britain". The term "United Kingdom" has been used as a description for the former kingdom of Great Britain, although its official name from 1707 to 1800 was "Great Britain"; the Acts of Union 1800 united the kingdom of Great Britain and the kingdom of Ireland in 1801, forming the United Kingdom of Great Britain and Ireland. Following the partition of Ireland and the independence of the Irish Free State in 1922, which left Northern Ireland as the only part of the island of Ireland within the United Kingdom, the name was changed to the "United Kingdom of Great Britain and Northern Ireland".
Although the United Kingdom is a sovereign country, Scotland and Northern Ireland are widely referred to as countries. The UK Prime Minister's website has used the phrase "countries within a country" to describe the United Kingdom; some statistical summaries, such as those for the twelve NUTS 1 regions of the United Kingdom refer to Scotland and Northern Ireland as "regions". Northern Ireland is referred to as a "province". With regard to Northern Ireland, the descriptive name used "can be controversial, with the choice revealing one's political preferences"; the term "Great Britain" conventionally refers to the island of Great Britain, or politically to England and Wales in combination. However, it is sometimes used as a loose synonym for the United Kingdom as a whole; the term "Britain" is used both as a synonym for Great Britain, as a synonym for the United Kingdom. Usage is mixed, with the BBC preferring to use Britain as shorthand only for Great Britain and the UK Government, while accepting that both terms refer to the United K
James Collins (bioengineer)
James J. Collins is an American bioengineer, the Termeer Professor of Medical Engineering & Science and Professor of Biological Engineering at MIT, he is one of the founders of the emerging field of synthetic biology, has made multiple synthetic biology breakthroughs in biotechnology and biomedicine, including paper-based diagnostics for Zika & Ebola and programmable cells that serve as living diagnostics and living therapeutics to detect-and-treat infections, rare genetic metabolic disorders, inflammatory bowel disease. Collins is a pioneering researcher in systems biology, having made fundamental discoveries regarding the actions of antibiotics and the emergence of antibiotic resistance. Collins received a bachelor's degree in physics from the College of the Holy Cross in 1987 and a doctorate in Medical Engineering from the University of Oxford in 1990. From 1987 to 1990, he was a Rhodes Scholar. Collins is the Termeer Professor of Medical Engineering & Science and Professor of Biological Engineering at MIT. Collins is a core founding faculty member of the Wyss Institute for Biologically Inspired Engineering at Harvard University and an Institute Member of the Broad Institute at MIT and Harvard.
From 1990 to 2014, he was on the faculty at Boston University, where he was a William F. Warren Distinguished Professor, a University Professor, Professor of Biomedical Engineering, Co-Director of the Center for BioDynamics and Director of the Center of Synthetic Biology. Collins' scientific accomplishments have been recognized by numerous awards, including the NIH Director's Pioneer Award, the Ellison Medical Foundation Senior Scholar Award in Aging, the inaugural Anthony J. Drexel Exceptional Achievement Award, the Lagrange Prize from the CRT Foundation in Italy, the Sanofi-Institut Pasteur Award, the BMES Robert A. Pritzker Award, the HFSP Nakasone Award, the Promega Biotechnology Research Award, being selected for Technology Review's inaugural TR100 - 100 young innovators who will shape the future of technology - and the Scientific American 50 - the top 50 outstanding leaders in science and technology. Collins is a Fellow of the American Physical Society, the Institute of Physics, the American Institute for Medical and Biological Engineering.
In 2003, he received a MacArthur Foundation "Genius Award", becoming the first bioengineer to receive this honor. Collins' award citation noted, "Throughout his research, Collins demonstrates a proclivity for identifying abstract principles that underlie complex biological phenomena and for using these concepts to solve concrete, practical problems.". He was honored as a Medical All-Star by the Boston Red Sox, threw out the first pitch at a Red Sox game in Fenway Park. In 2016, Collins was named an Allen Distinguished Investigator by the Paul G. Allen Frontiers Group. Collins is an elected member of all three U. S. national academies - the National Academy of Sciences, the National Academy of Engineering, the National Academy of Medicine. He is an elected fellow of the American Academy of Arts and Sciences, as well as a charter fellow of the National Academy of Inventors. Collins is a committed teacher, he has won numerous teaching awards at Boston University, including the Biomedical Engineering Teacher of the Year Award, the College of Engineering Professor of the Year Award, the Metcalf Cup and Prize for Excellence in Teaching, the highest teaching honor awarded by Boston University.
Collins has been involved with a number of start-up companies, his inventions and technologies have been licensed by several biotech and medical device companies. Collins is the scientific co-founder and chairs the Scientific Advisory Board of Sample6 Technologies, Synlogic and EnBiotix, he serves on the Board of Directors of Fulcrum Therapeutics and the SAB of Agilis Biotherapeutics, Evelo Biosciences, enEvolv, Indigo Agriculture, Joule Unlimited, PureTech Health and Excel Medical Ventures. Additionally, he has served on the SAB of Mannkind Corporation, Seres Health, Codon Devices, Gene Network Sciences, Epitome Biosystems, Afferent Corp, Cellicon Biotechnologies, Synereca Pharmaceuticals, LifeWave Ltd, Bios Group Inc. Collins has served as a science advisor to Unilever, Agilent, Momenta Pharmaceuticals, the New England Patriots, Brooks Sports. Collins ran track and cross country at Holy Cross, earned a blue playing for the varsity basketball team at the University of Oxford. Collins has pioneered the development and use of nonlinear dynamical approaches to study and improve biological function, helped to transform biology into an engineering science.
His current research interests include: synthetic biology - modeling and constructing synthetic gene networks, systems biology - reverse engineering occurring gene regulatory networks. Collins has invented a number of novel devices and techniques, including vibrating insoles for enhancing balance, a prokaryotic riboregulator, bistable genetic toggle switches for biotechnology and bioenergy applications, dynamical control techniques for eliminating cardiac arrhythmias, systems biology techniques for identifying drug targets and disease mediators. Collins proposed that input noise could be used to enhance sensory function and motor control in humans, he and collaborators showed that touch sensation and balance control in young and older adults, patients with stroke, patients with diabetic neuropathy could be improved with the application of sub-sensory mechanical noise, e.g. via vibrating insoles. This work has led to the creation of a new class of medical devices to address complications resulting from diabetic neuropathy, restore brain fun
India known as the Republic of India, is a country in South Asia. It is the seventh largest country by area and with more than 1.3 billion people, it is the second most populous country as well as the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives, while its Andaman and Nicobar Islands share a maritime border with Thailand and Indonesia; the Indian subcontinent was home to the urban Indus Valley Civilisation of the 3rd millennium BCE. In the following millennium, the oldest scriptures associated with Hinduism began to be composed. Social stratification, based on caste, emerged in the first millennium BCE, Buddhism and Jainism arose. Early political consolidations took place under the Gupta empires. In the medieval era, Zoroastrianism and Islam arrived, Sikhism emerged, all adding to the region's diverse culture.
Much of the north fell to the Delhi Sultanate. The economy expanded in the 17th century in the Mughal Empire. In the mid-18th century, the subcontinent came under British East India Company rule, in the mid-19th under British Crown rule. A nationalist movement emerged in the late 19th century, which under Mahatma Gandhi, was noted for nonviolent resistance and led to India's independence in 1947. In 2017, the Indian economy was the world's sixth largest by nominal GDP and third largest by purchasing power parity. Following market-based economic reforms in 1991, India became one of the fastest-growing major economies and is considered a newly industrialised country. However, it continues to face the challenges of poverty, corruption and inadequate public healthcare. A nuclear weapons state and regional power, it has the second largest standing army in the world and ranks fifth in military expenditure among nations. India is a federal republic governed under a parliamentary system and consists of 29 states and 7 union territories.
A pluralistic and multi-ethnic society, it is home to a diversity of wildlife in a variety of protected habitats. The name India is derived from Indus, which originates from the Old Persian word Hindush, equivalent to the Sanskrit word Sindhu, the historical local appellation for the Indus River; the ancient Greeks referred to the Indians as Indoi, which translates as "The people of the Indus". The geographical term Bharat, recognised by the Constitution of India as an official name for the country, is used by many Indian languages in its variations, it is a modernisation of the historical name Bharatavarsha, which traditionally referred to the Indian subcontinent and gained increasing currency from the mid-19th century as a native name for India. Hindustan is a Middle Persian name for India, it was introduced into India by the Mughals and used since then. Its meaning varied, referring to a region that encompassed northern India and Pakistan or India in its entirety; the name may refer to either the northern part of India or the entire country.
The earliest known human remains in South Asia date to about 30,000 years ago. Nearly contemporaneous human rock art sites have been found in many parts of the Indian subcontinent, including at the Bhimbetka rock shelters in Madhya Pradesh. After 6500 BCE, evidence for domestication of food crops and animals, construction of permanent structures, storage of agricultural surplus, appeared in Mehrgarh and other sites in what is now Balochistan; these developed into the Indus Valley Civilisation, the first urban culture in South Asia, which flourished during 2500–1900 BCE in what is now Pakistan and western India. Centred around cities such as Mohenjo-daro, Harappa and Kalibangan, relying on varied forms of subsistence, the civilization engaged robustly in crafts production and wide-ranging trade. During the period 2000–500 BCE, many regions of the subcontinent transitioned from the Chalcolithic cultures to the Iron Age ones; the Vedas, the oldest scriptures associated with Hinduism, were composed during this period, historians have analysed these to posit a Vedic culture in the Punjab region and the upper Gangetic Plain.
Most historians consider this period to have encompassed several waves of Indo-Aryan migration into the subcontinent from the north-west. The caste system, which created a hierarchy of priests and free peasants, but which excluded indigenous peoples by labeling their occupations impure, arose during this period. On the Deccan Plateau, archaeological evidence from this period suggests the existence of a chiefdom stage of political organisation. In South India, a progression to sedentary life is indicated by the large number of megalithic monuments dating from this period, as well as by nearby traces of agriculture, irrigation tanks, craft traditions. In the late Vedic period, around the 6th century BCE, the small states and chiefdoms of the Ganges Plain and the north-western regions had consolidated into 16 major oligarchies and monarchies that were known as the mahajanapadas; the emerging urbanisation gave rise to non-Vedic religious movements, two of which became independent religions. Jainism came into prominence during the life of Mahavira.
Buddhism, based on the teachings of Gautama Buddha, attracted followers from all social classes excepting the middle
Australia the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania and numerous smaller islands. It is the world's sixth-largest country by total area; the neighbouring countries are Papua New Guinea and East Timor to the north. The population of 25 million is urbanised and concentrated on the eastern seaboard. Australia's capital is Canberra, its largest city is Sydney; the country's other major metropolitan areas are Melbourne, Brisbane and Adelaide. Australia was inhabited by indigenous Australians for about 60,000 years before the first British settlement in the late 18th century, it is documented. After the European exploration of the continent by Dutch explorers in 1606, who named it New Holland, Australia's eastern half was claimed by Great Britain in 1770 and settled through penal transportation to the colony of New South Wales from 26 January 1788, a date which became Australia's national day; the population grew in subsequent decades, by the 1850s most of the continent had been explored and an additional five self-governing crown colonies established.
On 1 January 1901, the six colonies federated. Australia has since maintained a stable liberal democratic political system that functions as a federal parliamentary constitutional monarchy, comprising six states and ten territories. Being the oldest and driest inhabited continent, with the least fertile soils, Australia has a landmass of 7,617,930 square kilometres. A megadiverse country, its size gives it a wide variety of landscapes, with deserts in the centre, tropical rainforests in the north-east and mountain ranges in the south-east. A gold rush began in Australia in the early 1850s, its population density, 2.8 inhabitants per square kilometre, remains among the lowest in the world. Australia generates its income from various sources including mining-related exports, telecommunications and manufacturing. Indigenous Australian rock art is the oldest and richest in the world, dating as far back as 60,000 years and spread across hundreds of thousands of sites. Australia is a developed country, with the world's 14th-largest economy.
It has a high-income economy, with the world's tenth-highest per capita income. It is a regional power, has the world's 13th-highest military expenditure. Australia has the world's ninth-largest immigrant population, with immigrants accounting for 26% of the population. Having the third-highest human development index and the eighth-highest ranked democracy globally, the country ranks in quality of life, education, economic freedom, civil liberties and political rights, with all its major cities faring well in global comparative livability surveys. Australia is a member of the United Nations, G20, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, World Trade Organization, Asia-Pacific Economic Cooperation, Pacific Islands Forum and the ASEAN Plus Six mechanism; the name Australia is derived from the Latin Terra Australis, a name used for a hypothetical continent in the Southern Hemisphere since ancient times. When Europeans first began visiting and mapping Australia in the 17th century, the name Terra Australis was applied to the new territories.
Until the early 19th century, Australia was best known as "New Holland", a name first applied by the Dutch explorer Abel Tasman in 1644 and subsequently anglicised. Terra Australis still saw occasional usage, such as in scientific texts; the name Australia was popularised by the explorer Matthew Flinders, who said it was "more agreeable to the ear, an assimilation to the names of the other great portions of the earth". The first time that Australia appears to have been used was in April 1817, when Governor Lachlan Macquarie acknowledged the receipt of Flinders' charts of Australia from Lord Bathurst. In December 1817, Macquarie recommended to the Colonial Office. In 1824, the Admiralty agreed that the continent should be known by that name; the first official published use of the new name came with the publication in 1830 of The Australia Directory by the Hydrographic Office. Colloquial names for Australia include "Oz" and "the Land Down Under". Other epithets include "the Great Southern Land", "the Lucky Country", "the Sunburnt Country", "the Wide Brown Land".
The latter two both derive from Dorothea Mackellar's 1908 poem "My Country". Human habitation of the Australian continent is estimated to have begun around 65,000 to 70,000 years ago, with the migration of people by land bridges and short sea-crossings from what is now Southeast Asia; these first inhabitants were the ancestors of modern Indigenous Australians. Aboriginal Australian culture is one of the oldest continual civilisations on earth. At the time of first European contact, most Indigenous Australians were hunter-gatherers with complex economies and societies. Recent archaeological finds suggest. Indigenous Australians have an oral culture with spiritual values based on reverence for the land and a belief in the Dreamtime; the Torres Strait Islanders, ethnically Melanesian, obtained their livelihood from seasonal horticulture and the resources of their reefs and seas. The northern coasts and waters of Australia were visited s
David J. Julius is an American physiologist known for his work on molecular mechanisms underlying detection of thermal stimuli and natural products, he is a professor at the University of California, San Francisco, won the 2010 Shaw Prize in life science and medicine. A native of Brighton Beach, Julius earned his undergraduate degree from Massachusetts Institute of Technology in 1977, he attained his doctorate from University of California, Berkeley in 1984, under joint supervision of Jeremy Thorner and Randy Schekman. In 1989, he completed his post-doctoral training with Richard Axel at Columbia University where he cloned and characterized the serotonin 1c receptor. In 1997, the Julius lab cloned and characterized TrpV1, the receptor that detects capsaicin, the chemical in chili peppers that makes them "hot". Remarkably, they found that TrpV1 detects noxious heat. TrpV1 is part of the large family of structurally related TRP cation channels. Animals that lack TrpV1 loose sensitivity to noxious capsaicin.
The Julius lab has cloned and characterized TrpM8 and TrpA1, both members of the TRP superfamily. They demonstrated that cooler temperatures and TrpA1 detects mustard oil; these observations suggested that TRP channels could detect a range of chemicals. David Julius's lab has made important contributions to the study of nociception by discovering toxins that modulate these channels, describing unique adaptations of the channels in diverse species and solving the cryo-EM structures of numerous channels. In 2000, Julius was awarded the inaugural Perl-UNC Neuroscience Prize for his work on cloning the capsaicin receptor. In 2010, he won the Shaw Prize for his work identifying the ion channels involved in various aspects of nociception. In 2014 he was honored by Johnson & Johnson with the Dr. Paul Janssen Award for Biomedical Research for discovering the molecular basis for pain and thermosensation. In 2017, he won the HFRP Nakasone Award. Website at UCSF
United States dollar
The United States dollar is the official currency of the United States and its territories per the United States Constitution since 1792. In practice, the dollar is divided into 100 smaller cent units, but is divided into 1000 mills for accounting; the circulating paper money consists of Federal Reserve Notes that are denominated in United States dollars. Since the suspension in 1971 of convertibility of paper U. S. currency into any precious metal, the U. S. dollar is, de facto, fiat money. As it is the most used in international transactions, the U. S. dollar is the world's primary reserve currency. Several countries use it as their official currency, in many others it is the de facto currency. Besides the United States, it is used as the sole currency in two British Overseas Territories in the Caribbean: the British Virgin Islands and Turks and Caicos Islands. A few countries use the Federal Reserve Notes for paper money, while still minting their own coins, or accept U. S. dollar coins. As of June 27, 2018, there are $1.67 trillion in circulation, of which $1.62 trillion is in Federal Reserve notes.
Article I, Section 8 of the U. S. Constitution provides that the Congress has the power "To coin money". Laws implementing this power are codified at 31 U. S. C. § 5112. Section 5112 prescribes the forms; these coins are both designated in Section 5112 as "legal tender" in payment of debts. The Sacagawea dollar is one example of the copper alloy dollar; the pure silver dollar is known as the American Silver Eagle. Section 5112 provides for the minting and issuance of other coins, which have values ranging from one cent to 100 dollars; these other coins are more described in Coins of the United States dollar. The Constitution provides that "a regular Statement and Account of the Receipts and Expenditures of all public Money shall be published from time to time"; that provision of the Constitution is made specific by Section 331 of Title 31 of the United States Code. The sums of money reported in the "Statements" are being expressed in U. S. dollars. The U. S. dollar may therefore be described as the unit of account of the United States.
The word "dollar" is one of the words in the first paragraph of Section 9 of Article I of the Constitution. There, "dollars" is a reference to the Spanish milled dollar, a coin that had a monetary value of 8 Spanish units of currency, or reales. In 1792 the U. S. Congress passed a Coinage Act. Section 9 of that act authorized the production of various coins, including "DOLLARS OR UNITS—each to be of the value of a Spanish milled dollar as the same is now current, to contain three hundred and seventy-one grains and four sixteenth parts of a grain of pure, or four hundred and sixteen grains of standard silver". Section 20 of the act provided, "That the money of account of the United States shall be expressed in dollars, or units... and that all accounts in the public offices and all proceedings in the courts of the United States shall be kept and had in conformity to this regulation". In other words, this act designated the United States dollar as the unit of currency of the United States. Unlike the Spanish milled dollar, the U.
S. dollar is based upon a decimal system of values. In addition to the dollar the coinage act established monetary units of mill or one-thousandth of a dollar, cent or one-hundredth of a dollar, dime or one-tenth of a dollar, eagle or ten dollars, with prescribed weights and composition of gold, silver, or copper for each, it was proposed in the mid-1800s that one hundred dollars be known as a union, but no union coins were struck and only patterns for the $50 half union exist. However, only cents are in everyday use as divisions of the dollar. XX9 per gallon, e.g. $3.599, more written as $3.599⁄10. When issued in circulating form, denominations equal to or less than a dollar are emitted as U. S. coins while denominations equal to or greater than a dollar are emitted as Federal Reserve notes. Both one-dollar coins and notes are produced today, although the note form is more common. In the past, "paper money" was issued in denominations less than a dollar and gold coins were issued for circulation up to the value of $20.
The term eagle was used in the Coinage Act of 1792 for the denomination of ten dollars, subsequently was used in naming gold coins. Paper currency less than one dollar in denomination, known as "fractional currency", was sometimes pejoratively referred to as "shinplasters". In 1854, James Guthrie Secretary of the Treasury, proposed creating $100, $50 and $25 gold coins, which were referred to as a "Union", "Half Union", "Quarter Union", thus implying a denomination of 1 Union = $100. Today, USD notes are made from cotton fiber paper, unlike most common paper, made of wood fiber. U. S. coins are produced by the United States Mint. U. S. dollar banknotes are printed by the Bureau of Engraving and Printing and, since 1914, have been issued by t